Question

A system of inequalities, where x is the rate of a spaceship in a video game and y is where the ship travels on the screen in 3.5 seconds, is represented by the graph. On a coordinate plane, 2 solid straight lines are shown. The first line is vertical at x = negative 2. Everything to the right of the line is shaded. The second line has a positive slope and goes through (negative 2, negative 6) and (0, 0). Everything to the left of the line is shaded. Which symbol could be written in both circles in order to represent this system algebraically? y Circle 3x x Circle –2 ≤ ≥ < >

Answer 1

Answer:

Option B.

Step-by-step explanation:

On a coordinate plane, 2 solid straight lines and their shaded region are shown. We need to find the system of inequalities.

It is given that the first line is vertical at x = -2. Everything to the right of the line is shaded.  It means the value of x must be greater than or equal to -2.

$x\ge -2$

The second line has a positive slope and goes through (-2, -6) and (0, 0).

If a line passes through two points, then the equation of line is

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the point (0,0) and (-2,-6). The equation of line is

$y-0=\dfrac{-6-0}{-2-0}(x-0)$

$y=3x$

Everything to the left of the line is shaded. It means the sign of inequality is ≥.

$y\ge 3x$

Missing sign in both inequalities is ≥.

Therefore, the correct option is B.